# Tagged Questions

The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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### Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
251 views

### Calculate the entropy per atom in Bohmian Mechanics

Bohmian mechanics description of a large number of interacting atoms would require a large phase space due to the large number of classical degrees of freedom. The entropy per atom is given as the ...
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### Gibbs' Free Energie

What terms are needed to consider to create a rabbit out of nothing and place it in the classroom? Does this caption answer the question?
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### Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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### Maxwell velocity distribution, in 1D or otherwise

I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$ Presumably this is for a three dimensions. This confuses ...
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### Hindered rotation model for flexible polymers: deriving the Flory characteristic ratio

In the hindered rotation model we assumes constant bond angles $\theta$ and lengths $\ell$, with torsion angles between adjacent monomers being hindered by a potential $U(\phi_i)$. In Rubinstein's ...
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### A micro-reversible stochastic process that models transitions between states with variable energies

Suppose we have a system with 3 possible states A, B and C (there could be $n$ states as well) with energies $E_a(t)$, $E_b(t)$ and $E_c(t)$ that vary with time. If our system has a constant finite ...
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### Why is the average thermal velocity 0?

Thermal velocity is the velocity of the free electron due to their random motion. So how is the average value 0?
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### Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
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### What is the difference between these two expressions for the partition function, Z?

What is the difference between these two expressions given for the partition function, Z? $$Z = \sum_{i}e^{-\varepsilon_i/kT}$$ $$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$ where each energy level has ...
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### Triangular and Kagome lattice anti ferromagnet at zero temperature

The triangular lattice with anti ferromagnetically coupled nearest neighbour ising spins has a power law ordered zero temperature state at the three sublattice wavevector. Kagome lattice, with the ...
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### Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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### Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
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### Poincare recurrence time of the Universe

I've read around a bit, and it seems to be universal that the notion of a Poincare recurrence time for the universe exists. And it seems to be debated that the universe can be given an entropy, as it ...
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### Is it possible for a system to become irreversible?

Imagine a ball bouncing in a box for a long time. We know, there is a certain path it can go to bounce off infinitely (see the image). If it gets to this state, it will never be able to get back again....
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### Time Scales Of Processes In Molecular Dynamics

Suppose I run a molecular dynamics simulation of a fluid sandwiched between solid walls which are periodic in the lateral directions and finite in the direction of the fluid film thickness. Now, I ...
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### boltzmann weight factor and statistical ensembles

i am working on a project about in-equivalence between statistical ensembles ( micro-canonical and canonical to be more precise ). how can we show that the in the canonical ensemble the system is ...
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### Does entropy always increase with temperature? [duplicate]

For any system can we always say that entropy increases with temperature. In other words: $$\left(\frac{\partial S}{\partial T} \right)_{\{\alpha\}}\ge0$$ where $\{\alpha\}$ is the set of parameters ...
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### Why do we have this difference in the multiplicity of Cartesian space and momentum space for a gas?

For an ideal gas, the multiplicity of an ideal gas with $N$ molecules in Cartesian space is $$\Omega_{\text{space}}=\Big(\frac{V}{(\Delta x)^3}\Big)^N.$$ This is pretty intuitive, because we are ...
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### Obtaining the temperature from Bose-Einstein and Fermi-Dirac distribution

Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.) It is then natural to define a temperature the ...
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### Is there anything comparable to many-body localization in classical physics?

I've only just started looking into many-body localization, so this question may come off as a little vague. But my understanding is that it relates to how some quantum systems do not thermalize, as ...
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### The calculation of the entropy of a single atom

I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated. But my professor told me the entropy ...
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### If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
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### Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
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### Rugged Energy Landcapes (Free Energy vs Potential Energy Questions)

A spin glass has what is called a "rugged energy landscape." That is, when you cool down below a certain temperature, the system divides into many wells, all corresponding to slightly different ...
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### How do inverse of Kirchoff matrix of a polymer possess the information for its mobility?

In Normal Mode Analysis of polymers like proteins, I have seen that mobility (measures like root mean squared fluctuations) can be found from the eigen values and eigen vectors of inverse of Kirchoff ...
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### Operator formalism in QFT in Euclidean space-time

In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one ...
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### Deriving Ideal Gas law from Hamiltonian Mechanics

I just don't understand the explanation in Wikipedia. Is there a nice & elegant way of arriving at the Ideal Gas Law from Hamilton's Equations?
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### When does the Boltzmann distribution apply?

What are the requirements for a system to be described by the Boltzmann distribution in equilibrium? For example, should all the particles be identical? No attractors in the phase space? ...
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### Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
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### Entropy for $N$ number of particles [closed]

If there are $N$ number of non-interacting and distinguishable particles which have either Energy $E_1$ or $E_2$ , then a. What will be the entropy $S(n)$ for such system? ($n$ is the number of ...
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### Extensiveness of entropy in classical microcanonical ensemble

In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form $S(V,E) = k \log \Gamma(V,E)$, where $\Gamma$ ...
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### A conceptual question related to statistical mechanics

Statistical mechanics allows us to consider an ensemble of systems, each of which consisting of only a single particle. Once we write the partition function for the system of one particle, we can ...
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### Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
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### Why do Temperatures Equalize

I have some Oxygen at Temp A in one container and some Nitrogen at Temp B in another container. If I mix these two containers eventually both the Oxygen and Nitrogen will be at the same temperature. ...
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### White noise in the Langevin model and it's autocorrelation function

I am having some trouble understanding and interpreting the noise term in the Langevin equation for a colloidal particle in a fluid. By the Langevin model, I mean the following model as the equation ...